On the regularization of SENSE and Space-RIP in parallel MR imaging

Parallel imaging methods provide accelerated multiple coil MR image acquisitions via reconstruction of sub-sampled k-space data. Currently, analytic comparison between different reconstruction approaches has been hampered by use of different phase encoding paradigms and regularization approaches, historically unique to each method. We present an analysis of the Space-RIP image reconstruction problem that demonstrates the ability to recast the problem in a decoupled form when uniform down-sampling is employed. We show that this decoupled problem is equivalent to the SENSE image reconstruction approach. This approach enables a clear analytic comparison between SENSE and Space-RIP, and we demonstrate the effect of different regularization approaches on image formation in low coil sensitivity regions.